There are numerous physical phenomena affecting performance of electronic circuits such as, for example, thermal noise in resistors, oscillations in power supplies, interference signals in transceivers, and jitter in clocks. Based on the Central Limit Theorem, which states that even when individual random variables are not normally distributed their sums and averages will tend to follow a normal distribution, it is in many situations possible to model these physical phenomena using a Gaussian Probability Distribution Function (PDF). Being able to accurately model these physical phenomena is paramount in testing of present day electronic circuits and their components. A Gaussian noise generator has a wide variety of applications ranging from electronic testing and modeling to communication channel emulation. For example, it is possible to use a Gaussian noise source for determining a Bit Error Rate (BER) in digital communication channels. Furthermore, it has been shown in G. Evans, J. Goes, and N. Paulino: “On-Chip Built-in Self-Test of Video-Rate ADCs using a 1.5 V CMOS Noise Generator”, IEEE ISCAS, 2005, pp. 796-799, how histogram testing using a Gaussian noise test signal is performed for DNL/INL measurements in video-rate Analog-to-Digital Converters (ADCs).
Typically, analog Gaussian noise signals are generated either by low-pass filtering the output signal of a Linear Feedback Shift Register (LFSR)—first method—or by amplifying the thermal noise of a resistor—second method. Unfortunately, both these methods do not allow a user to define the characteristics—mean and standard deviation of the probability distribution function—of the Gaussian noise signal. Furthermore, the Gaussian noise signal generated using the first method does not accurately follow a Gaussian PDF and the Gaussian noise signal generated using the second method is substantially affected by process variations such as temperature of the resistor. Digital implementations of pseudo-random Gaussian signal sources employing, for example, the Box-Muller method have successfully been realized. However, converting the multi-bit Gaussian pseudo-random numbers into an analog Gaussian noise signal is not a trivial task requiring a highly complex Digital-to Analog conversion satisfying very stringent specifications.
It would be highly desirable to overcome the above limitations of the state of the art and to provide a simple method and system for generating an analog Gaussian noise signal that allows a user to determine the mean and the standard deviation of its PDF.